Question

Calculate median from the following:

Marks (less than)	5	10	15	20	25	30	35	40	45
No. of Students	3	11	16	32	58	70	76	79	80

Answer 1

Class Interval	Cumulative Frequency (c.f.)	Frequency (f)
0 − 5 5 − 10 10 − 15 15 − 20	3 11 16 32 (c.f.)	3 8 5 16
20 − 25	58	26 (f)
25 − 30 30 − 35 35 − 40 40 − 45	70 76 79 80	12 6 3 1
	N=80

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{80}{2}\right)}^{\mathrm{th}}$ item, which is 40^th item.
This corresponds to the class interval of 20 − 25, so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{80}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=20+\frac{40-32}{26}\times 5 \\ \mathrm{or},\mathrm{Median}=20+1.538=21.538 \\ \mathrm{Thus},\mathrm{Median}=21.54 \end{gathered}$$